The position of generalized offset curves in technology

Due to the significant importance of offset curves in applications such as technology, engineering, and computer-aided geometric design, our thesis predominantly focuses on investigations conducted on planar curves. Generalized offset curves and intersection curves are addressed in detail. Generalized offset curves and nth-degree generalized offset curves are examined, accompanied by practical applications of these curves. Topics such as intersection scenarios of curves and computation of singularities are discussed. Additionally, the representation of generalized offset curves and nth-degree generalized offset curves in terms of standard offset curves is scrutinized and supported by propositions. Furthermore, in the analysis of complex geometric structures, higher-order approaches are necessary for the accurate and efficient calculation of intersection curves. Within this framework, separate examinations are conducted for planar curves, spatial curves, and intersection curves concerning generalized offset curves. Supported by definitions and applications, this thesis aims to contribute to the literature by elucidating the fundamental concepts of offset curves and generalized offset curves, thus enriching the fields of computer-aided geometric design and differential geometry.